We had a problem in class that said that through a given line on plane A there is only one plane that intersects plane B (not dealing with my pictures). I thought there would be an infinite amount of planes.

We had a problem in class that said that through a given line on plane A there is only one plane that intersects plane B (not dealing with my pictures). I thought there would be an infinite amount of planes.

Was there more to the problem? Imagine rotating the plane around the line where it intersects A. That will give an infinite number of planes that still intersect B.